Metamaterial beam with dual-action absorbers for tunable and multi-band vibration absorption

This paper presents a new class of metamaterial beams of tunable and multi-band vibration absorption. The metamaterial beam is composed of uniform and periodic beam cells with locally resonant substructure called dual-action vibration absorber, DA. A DA vibration absorber comprising of three locally resonant subsystems, 3-DOF spring-mass-damper subsystems, is utilized to generate frequency stopbands to stop elastic wave propagation. The governing equations of motion for a periodic beam cell are derived. Several distinct mass and stiffness configurations for the metamaterial beam with DA vibration absorber are proposed. The dispersion relations and presence of three frequency stopbands are studied. A finite element method based on Timoshenko beam theory is used to model and analyze the introduced metamaterial beam with DA vibration absorber. The frequency response simulations agree well with the projected stopbands of the developed dispersion relations of the mass and stiffness configurations. The concept of the presented metamaterial beam with tunable and multi-stopbands is promising for wave propagation attenuation and control applications.